Wavelengths Debye scattering

Elastically scattered radiation reaching a detector from different scattering centers in a macromolecule will be subject to interference effects, provided the dimensions of the macromolecule are comparable to or larger than the wavelength of the radiation (22). The Debye scattering function P(u) describes the variation, arisir from intramolecular interference effects, of the scattered... 

Micelles are small, relative to the wavelength of light. Their solutions are therefore transparent, but they scatter light, and this property provided compelling evidence for the formation of discrete micelles (Debye, 1949 Debye and Anacker, 1951). 

The spectral distribution of light scattered from a plasma depends on its wavelength Xq, the electron Debye length and the scattering... 

S is the scattering vector, Mj is the atomic displacement parameter in this simplified notation assumed to be isotropic, 6 is the scattering angle, and 1 the wavelength of the incident radiation. The atomic displacement depends on the temperature, and hence so does the Debye-Waller factor. If an atom is modeled by a classical oscillator, then the atomic displacement would change linearly with temperature ... 

Mie wrote the scattering and absorption cross sections as power series in the size parameter 0, restricting the series to the first few terms. This truncation of the series restricts the Mie theory to particles with dimensions less than the wavelength of light but, unlike the Rayleigh and Debye approximations, applies to absorbing and nonabsorbing particles. 

From optics we know that diffraction only occurs if the wavelength is comparable to the separation of the scatterers. In 1912, Friedrich, Knipping and Max von Laue performed the first X-ray diffraction experiment using single crystals of copper sulfate and zinc sulfite, proving the hypothesis that X-rays are em-waves of very short wavelength, on the order of the separation of the atoms in a crystalline lattice. Four years later (1916), Debye and Scherrer reported the first powder diffraction pattern with a procedure that is named after them. 

Analytical expressions for the particle scattering factor P (0 ) are required so that an appropriate extrapolation to 0 = 0 can be performed in order to eliminate the effects of interference. Debye showed that the functional form of P(0) depends on the shape of the scatterers. The following scattering functions have been derived for three models in terms of a polymer dimension, the wavelength of the light, and the refractive index of the solvent [7]. 

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